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**Geometry Trigonometry**

Do Bees Build It Best? Geometry Trigonometry

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BUILDING THE BEST

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NAILING DOWN AREA

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HOW MANY CAN YOU FIND?

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THAT’S ALL THERE IS!

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HALVING YOUR WAY

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**PARALLELOGRAMS AND TRAPEZOIDS**

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FORMING FORMULAS

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GOING INTO THE GALLERY

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**A RIGHT-TRIANGLE PAINTING**

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**A TRIGONOMETRIC SUMMARY**

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**MORE GALLERY MEASUREMENTS**

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A HOMEMADE TRIG TABLE

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SHADOWS AND SAILBOATS

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TRI-SQUARE RUG GAMES

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ANY TWO SIDES WORK LEG^2 + LEG^2 = HYP^2

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IMPOSSIBLE RUGS

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MAKE THE LINES COUNT

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PROOF BY RUGS

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**THE POWER OF PYTHAGORAS**

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**LESLIE’S FERTILE FLOWERS**

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**FLOWERS FROM DIFFERENT SIDES**

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DON’T FENCE ME IN

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RECTANGLES ARE BORING!

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**MORE FENCING, BIGGER CORRALS**

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**MORE OPINIONS ABOUT CORRALS**

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**BUILDING THE BEST FENCE**

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FALLING BRIDGES

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**LESLIE’S FLORAL ANGLES**

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FLAT CUBES

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FLAT BOXES

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A VOLUMINOUS TASK

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PUT YOUR FIST INTO IT

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**THE INS AND OUTS OF BOXES**

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A SCULPTURE GARDEN

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THE WORLD OF PRISMS

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**SHEDDING LIGHT ON PRISMS**

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PYTHAGORAS AND THE BOX

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BACK ON THE FARM

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WHICH HOLDS MORE?

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CEREAL BOX SIZES

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A-TESSELLATING WE GO

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**A PORTFOLIO OF FORMULAS**

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**THAT’S ALL THERE IS! EACH TRIANGLE MUST HAVE AN AREA OF 2 UNITS**

EACH TRIANGLE MUST HAVE ITS VERTICES ON PEGS EACH TRIANGLE MUST HAVE A HORIZONTAL SIDE

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HALVING YOUR WAY

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FORMING FORMULAS LOOK FOR WAYS TO CUT UP THE PARALLELOGRAMS AND TRAPEZOIDS INTO TRIANGLES

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GOING INTO THE GALLERY REMEMBER, THE HEIGHT IS ALSO THE ALTITUDE WHICH IS DRAWN PERPENDICULAR TO THE BASE

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**A RIGHT-TRIANGLE PAINTING**

DRAW A RIGHT TRIANGLE THAT HAS A 55 DEGREE ANGLE EXTEND BOTH SIDES SO THAT THEY ARE AT LEAST 10 CM IN LENGTH

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**A TRIGONOMETRIC SUMMARY**

SIN A = OPPOSITE/HYPOTENUSE COS A = ADJACENT/HYPOTENUSE TAN A = OPPOSITE/ADJACENT

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A HOMEMADE TRIG TABLE DRAW A RIGHT TRIANGLE USING THE ASSIGNED ANGLE FOR YOUR GROUP MEASURE ALL THE SIDES COMPUTE THE RATIOS OF SIN, COS, AND TAN

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**MORE GALLERY MESUREMENTS**

SIN A = OPPOSITE/HYPOTENUSE COS A = ADJACENT/HYPOTENUSE TAN A = OPPOSITE/ADJACENT

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SHADOWS AND SAILBOATS

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TRI-SQUARE RUG GAMES AL WINS WHEN THE LARGEST OF THE 3 SQUARES HAS THE MOST AREA. WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

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TRI-SQUARE RUG GAMES BETTY WINS IF THE TWO SMALLER SQUARES HAVE MORE AREA THEN THE LARGEST WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

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TRI-SQUARE RUG GAMES IF THE TWO SMALLER SQUARES HAVE THE SAME AREA AS THE LARGEST, THIS IS A FAIR GAME. WHAT KIND OF TRIANGLE IS FORMED IN THIS SITUATION?

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ANY TWO SIDES WORK

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ANY TWO SIDES WORK

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ANY TWO SIDES WORK

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IMPOSSIBLE RUGS RULE: ANY TWO SIDES OF A TRIANGLE MUST BE GREATER THAN THE THIRD SIDE

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MAKE THE LINES COUNT

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**THE POWER OF PYTHAGORAS**

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**THE POWER OF PYTHAGORAS**

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**LESLIE’S FERTILE FLOWERS**

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**FLOWERS FROM DIFFERENT SIDES**

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**DON’T FENCE ME IN RANCHER GONZALES CAN ONLY AFFORD 300 FEET OF FECNING**

MAKE AN INOUT TABLE OF VARIOUS LENGTHS AND WIDTHS

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RECTANGLES ARE BORING! RANCHER GONZALE’S NEPHEW JUAN HAS SUGGESTED RECTANGLES AGAIN SHE MUST USE 300 FEET OF FENCING

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**MORE FENCING, BIGGER CORRALS**

HOW DOES THE AREA OF A SQUARE CORRAL MADE 300 FT OF FENCING COMPARE TO 600 FT?

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**MORE FENCING, BIGGER CORRALS**

HOW DOES THE AREA OF A AN EQUILATERAL TRIANGLE CORRAL MADE 300 FT OF FENCING COMPARE TO 600 FT?

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**MORE OPINIONS ABOUT CORRALS**

ACES : PENTAGON TWO’S: HEXAGON THREE’S: SEPTAGON FOUR’S: OCTAGON FIVE’S: 9 SIDED REG-POLY SIXE’S: 10 SIDED REG-POLY

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**BUILDING THE BEST FENCE**

AREA= (P^2/4n) * tan (90-180/n)

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FALLING BRIDGES USE OTHER APPROXIMATIONS FOR THE SQUARE ROOT OF 2

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**LESLIE’S FLORAL ANGLES**

REMEMBER, THE INVERSE OF: ADDING? MULTIPLYING? SOMETHING SQUARED? NOW WE NEED THE INVERSE OF OUR TRIG FUNCTIONS

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FLAT BOXES 132 CM SQUARED

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FLAT BOXES 108 CM SQUARED

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A VOLUMINOUS TASK SURFACE AREA VOLUME #1 #2 #3 #4 #5

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A VOLUMINOUS TASK SURFACE AREA VOLUME #7 #8 #9 #10

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PUT YOUR FIST INTO IT

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**THE INS AND OUTS OF BOXES**

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A SCULPTURE GARDEN FIND A WAY TO ARRANGE 8 CUBES THAT USES THE LEAST AMOUNT OF PAINT

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**THE WORLD OF PRISMS PRISM IS A SPECIAL TYPE OF SOLID GEOMETRIC FIGURE**

THE INTIAL AND FINAL FACES ARE THE BASES USUALLY 1 OR 2 BASES PERPENDICULAR DISTANCE BETWEEN THE BASES IS THE HEIGHT

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**THE WORLD OF PRISMS TRIANGULAR PRISMS HEXAGONAL PRISMS**

RECTANGULAR PRISMS

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THE WORLD OF PRISMS RIGHT PRISMS OBLIQUE PRISMS

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**THE WORLD OF PRISMS LATERAL FACES LATERAL EDGES BASES**

LATERAL SURFACE AREA TOTAL SURFACE AREA

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PYTHAGORAS AND THE BOX

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BACK ON THE FARM

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